When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx, Gy and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
In an magnetic resonance imaging sequence, a uniform magnetic field B0 is applied to an imaged object along the z axis of a Cartesian coordinate system. The effect of the magnetic field B0 is to align the object's nuclear spins along the z axis. In this field, the nuclei resonate at their Larmor frequencies according to ω=γB0, where ω is the Larmor frequency, and γ is the gyromagnetic ratio which is a property of the particular nucleus. The nuclei respond to RF pulses at this frequency by tipping their longitudinal magnetization into the transverse, x-y plane. Hydrogen (protons) in water, because of its relative abundance in biological tissue and the properties of its proton nuclei, is the imaging species of choice for most MRI applications. The value of the gyromagnetic ratio γ for protons in water is 4.26 kHz/Gauss and therefore in a 1.5 Tesla polarizing magnetic field B0, the resonant or Larmor frequency of water protons is approximately 63.9 MHz.
Materials other than water, principally fat, are also to be found in biological tissue and have different gyromagnetic ratios. The Larmor frequency of protons in fat is approximately 210 Hz lower than that of protons in water in a 1.5 Tesla polarizing magnetic field B0. The difference between the Larmor frequencies of such different isotopes or species of the same nucleus, namely protons, is termed chemical shift, reflecting the differing chemical environments of the two species.
In the well known slice selective RF pulse sequence, a slice selective magnetic field gradient Gz is applied at the time of the RF pulse so that only the nuclei in a slice through the object in an x-y plane are excited. After the excitation of the nuclei, magnetic field gradients are applied along the x and y axes and an NMR signal is acquired. The readout gradient Gx along the x axis causes the nuclei to precess at different resonant frequencies depending on their position along the x axis; that is, Gx spatially encodes the precessing nuclei by frequency. But because water and fat spins resonate at different frequencies, even when they are in the same location, their locations in the reconstructed image will be shifted with respect to each other. This is particularly problematic on the boundaries of tissues or organs where this chemical shift can cause blurring or multiple edges.
There is a large body of work that has been developed to selectively suppress certain signals such as the signals from fat. Reliable and uniform fat suppression is essential for accurate diagnoses in many areas of MRI. This is particularly true for MRI applications using certain pulse sequences such as fast spin-echo (FSE), steady-state free precession (SSFP) and gradient echo (GRE) imaging, in which fat is bright in the resultant images and may obscure underling pathology. Although conventional fat saturation may be adequate for areas of the body with a relative homogeneous B0 field, there are applications in which fat saturation routinely fails. This is particularly true for extremity imaging, off-isocenter imaging, large field of view (FOV) imaging, and challenging areas such as the brachial plexus and skull based, as well as many others. Short-TI inversion recovery (STIR) imaging provides uniform fat suppression, but at a cost of reduced signal-to-noise ratio (SNR) for the water image and mixed contrast that is dependent on T1, (Bydder G M, Pennock J M, Steiner R E, Khenia S, Payne J A, Young I R, The Short T1 Inversion Recovery Sequence-An Approach To MR Imaging Of The Abdomen, Magn. Reson. Imaging 1985; 3(3):251-254). This latter disadvantage limits STIR imaging to T2 weighted (T2W) applications, such that current T1 weighted (T1W) applications rely solely on conventional fat-saturation methods. Another fat suppression technique is the use of spectral-spatial or water selective pulses; however, this method is also sensitive to field inhomogeneities, (Meyer C H, Pauly J M, Macovski A, Nishimura D G, Simultaneous Spatial And Spectral Selective Excitation, Magn. Reson. Med. 1990; 15(2):287-304).
Other techniques have also been developed to obtain separate water and/or fat images. For example, “In and Out of Phase” Imaging was first described by Dixon in 1984, and is used to exploit the difference in chemical shifts between water and fat in order to separate water and fat into separate images, Dixon W. Simple Proton Spectroscopic Imaging, Radiology 1984; 153:189-194. Glover et al. further refined this approach in 1991 with a 3 point method that accounts for magnetic field inhomogeneities created by susceptibility differences, Glover G H, Schneider E, Three-Point Dixon Technique For True Water/Fat Decomposition With B0 Inhomogeneity Correction, Magn. Reson. Med. 1991; 18(2):371-383; Glover G, Multipoint Dixon Technique For Water and Fat Proton and Susceptibility Imaging, Journal of Magnetic Resonance Imaging 1991; 1:521-530. Hardy et al first applied this method with FSE imaging by acquiring three images with the readout centered at the spin-echo for one image and symmetrically before and after the spin-echo in the subsequent two images, Hardy P A, Hinks R S, Tkach J A, Separation Of Fat And Water In Fast Spin-Echo MR Imaging With The Three-Point Dixon Technique, J. Magn. Reson. Imaging 1995; 5(2):181-195.
Also recently, a water-fat separation method known as IDEAL (Iterative Decomposition of water and fat with Echo Asymmetry and Least squares estimation) has been described by Reeder S, Pineda A, Wen Z, et al., in Iterative Decomposition of Water and Fat With Echo Asymmetry and Least-Squares Estimation (IDEAL): Application with Fast Spin-echo Imaging, Magn Reson Med 2005; 54(3);636-644. IDEAL is an SNR-efficient method that uses flexible echo spacings and when combined with optimized echo spacings can provide the best possible SNR performance.
In addition to separation of water and fat, the accurate quantification of fat, especially in the liver, is an increasingly important unmet need. Nonalcoholic fatty liver disease is a term that incorporates a spectrum of histologic findings ranging from simple steatosis (fatty infiltration) to fibrosis, cirrhosis and liver failure. Nonalcoholic steatohepatitis is an intermediate stage characterized by steatosis and hepatic cell inflammation. These liver changes can progress to cirrhosis and even death, such that it is desirable to be able to accurately measure fat in the liver in order to provide early treatment and prevent progression of the disease. Currently, the definitive diagnosis of nonalcoholic fatty liver disease is determined with a liver biopsy.
MRI is a non-invasive method that can also be used to detect fatty infiltration of the liver, although quantification of fat in the liver has been limited, due to limitations in estimation of water and fat signals, including the effects of image noise bias, as explained below.
Consider the signal model for a voxel containing water (W) and fat (F), with a chemical shift frequency of Δf, which depends on the magnitude of the magnetic field B0 (e.g., −210 Hz at 1.5 T and −420 Hz at 3 T), acquired at an echo time of tn:s(tn)=(WeiφW+FeiφF·ei2πΔf tn)ei2πψtn   Equation 1
where φW is the time-independent phase of water and φF is the time independent phase of fat, and these phases can be unequal to each other; ψ is the local field inhomogeneity map (Hz); and W and F are real.
If a number N of images are acquired corresponding to different echo times tn, then methods such as IDEAL can be used to provide an estimate of the field inhomogeneity map ψ, demodulate the effects of the field map from the signal and subsequently decompose the water and fat signals into different images, i.e., to provide estimates of a complex water component Ŵ=WeiφW, and a complex fat component, {circumflex over (F)}=FeiφF.
There are several advantages to using the above signal model and allowing the phase of water and fat to be independent. The major advantage is that errors in the presumed chemical shift between water and fat (denoted by Δf) will manifest primarily as phase errors in these complex components Ŵ and {circumflex over (F)}, rather than as magnitude errors. For many applications, accurate estimation of the magnitude of water and fat signals is far more important. Therefore, although the phase angles could be set equal to one another, for estimation purposes, it is preferred that they be independent. Then, in order to calculate the fat fraction η, defined as:
                              η          =                      F                          F              +              W                                      ,                            Equation        ⁢                                  ⁢        2            The magnitudes of complex quantities Ŵ and {circumflex over (F)} are calculated (i.e. |Ŵ| and |{circumflex over (F)}|) and used to calculate the fat fraction according to:
                    η        =                                                                          F                ^                                                                                                                    F                  ^                                                            +                                                                W                  ^                                                                              .                                    Equation        ⁢                                  ⁢        3            